Quantification of heritability - the relationship between inherited genetics and phenotype - is an important first step to understanding the overall genetic contributions to complex disease. Recently, techniques using variance-components analysis have allowed researchers to effectively estimate the relationship between common markers and phenotype by leveraging thousands of unrelated individuals. This proposal focuses on local heritability analysis, where heritability is estimated from regions of the genome implicated as causal in genome-wide association studies or otherwise biologically significant. Previous biological work has shown multiple instances where deep re-sequencing of known loci uncovered an abundance of new causal variants, in some instances nearly doubling the amount of explained variance and revealing heterogeneity of causal variants at individual loci. However, these studies have not always been successful, and computationally answering the question of which loci harbor additional underlying variation can prioritize such fine-mapping analysis and guide overall association study-design. This proposal outlines novel statistical methods that use variance-components analysis to make these inferences for fine-mapping. The application of heritability techniques to this domain is novel, and my first aim is to quantify the amount of power this kind of analysis has as compared to standard estimating techniques using one or a handful of significant markers. I will apply these techniques to several diverse disease datasets with known associated loci and quantify the amount of additional variation likely to be hidden at these loci. I will use these findings to prioritize phenotypes and loci for follow-up study, and extrapolate to the expected outcome of larger studies. My second aim deals with a specific phenomenon associated with these techniques, where estimates become biased in the presence of markers that are correlated due to linkage-disequilibrium (LD). As such correlation is ubiquitous in real data and can be highly structured with respect to the disease causing variants, it is vitally important to address this bias. I propose several techniques from the population genetics domain which address correlation and detail further analysis of the impact of this bias on estimates of heritability, as well as down-stream techniques such as risk prediction and mixed-model association. Lastly, I describe an approach for capturing all of the heritability underlying a locus by looking at higher level relationships between individuals. Rather than estimate only over the markers that have been typed, I will attempt to infer the total amount of sharing between individuals by looking at combinations of markers. I will explore the demographic and cohort parameters that yield power to this technique and compare total heritability inferences to the other procedures described previously.